You can root the Amazon Kindle Fire HD or install custom ROMs such as CyanogenMod on the tablet. But if you want the best of both worlds, there’s a new app called KindleFree which simplifies the process of installing an alternate app launcher on a Kindle Fire HD running Amazon’s stock software.
KindleFree installs a custom launcher and the Google Play Store on a Kindle Fire HD tablet. There’s also an option to remove lockscreen ads from the Kindle home screen.
You can find instructions for rooting the Kindle Fire HD at the xda-developers section.